N-Dimensional Geometry

A tiny Python library for n-dimensional shape calculations.

Origin Story

This started as an 84-line Java assignment in CS102 (Fall 2014) to calculate sphere volume and surface area. Eleven years and much over-engineering later, we've returned to simplicity: ~150 lines of Python that actually do something useful.

The original Java is preserved in src/java/original/ for historical purposes.

Installation

# The library itself needs nothing - pure Python 3.8+
# For MCP server integration with Claude Desktop:
pip install "mcp[cli]"

Usage

As a Library

from ndgeometry import Sphere, Cube, Ellipsoid, Simplex

# 4D sphere
s = Sphere(dimensions=4, radius=2.0)
print(f"Volume: {s.volume}")        # 39.478...
print(f"Surface: {s.surface_area}") # 78.956...

# 3D cube
c = Cube(dimensions=3, side=2.0)
print(f"Volume: {c.volume}")    # 8.0
print(f"Diagonal: {c.diagonal}") # 3.464...

# Ellipsoid with different axes
e = Ellipsoid(semi_axes=(1.0, 2.0, 3.0))
print(f"Volume: {e.volume}")  # 25.132...

# Fun fact: unit sphere volume peaks at 5D!
for n in range(1, 10):
    print(f"{n}D: {Sphere(n, 1.0).volume:.4f}")

As an MCP Server (Claude Desktop)

Add to your claude_desktop_config.json:

{
  "mcpServers": {
    "geometry": {
      "command": "python",
      "args": ["F:\\utility-projects\\2014_CS102\\mcp_server.py"]
    }
  }
}

Then ask Claude things like:

• "What's the volume of a 7-dimensional sphere with radius 3?"
• "Compare a 4D sphere to a 4D cube with the same 'size'"
• "Show me how sphere volume changes from 1D to 15D"

Available Shapes

Shape	Class	Key Properties
N-sphere	Sphere(dimensions, radius)	volume, surface_area, diameter
N-cube	Cube(dimensions, side)	volume, surface_area, diagonal, vertices, edges
N-ellipsoid	Ellipsoid(semi_axes)	volume, is_sphere
N-simplex	Simplex(dimensions, side)	volume, vertices, edges

The Math

Sphere Volume

The volume of an n-dimensional unit ball is:

$$V_n = \frac{\pi^{n/2}}{\Gamma(n/2 + 1)}$$

For a sphere of radius r: $V = V_n \cdot r^n$

Cube Volume

Simply: $V = s^n$ where s is the side length.

The Curse of Dimensionality

A fascinating result: for a unit sphere, volume increases up to about 5D, then decreases toward zero as dimensions increase. This is why machine learning in high dimensions is hard - most of the "space" is near the edges.

Running Tests

python -m pytest test_ndgeometry.py -v

Files

ndgeometry.py          # The library (~150 lines)
mcp_server.py          # MCP server for Claude Desktop (~160 lines)
src/java/original/     # The original 2014 CS102 Java code
  Sphere.java
  MultiSphere.java

What We Threw Away

The previous version had:

• 2,300+ lines of geometry engine
• AWS Lambda + API Gateway + DynamoDB
• A regex-based "natural language" parser
• Runtime Java compilation
• 12 specialized ignore files
• 338-line .gitignore
• Incomplete Voronoi diagrams
• Documentation for features that didn't exist

Now we have ~300 lines total that actually work.

License

MIT - see LICENSE

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"Perfection is achieved not when there is nothing more to add, but when there is nothing left to take away." — Antoine de Saint-Exupéry